An unbound iron atom emits a Kα X-ray photon of energy 6.4 keV. Its recoil kinetic energy is approximately n × 10⁻⁴ eV. Find n.
Physics · Mixed Chapter
JEE Mains

Question

An unbound iron atom emits a Kα X-ray photon of energy 6.4 keV. Its recoil kinetic energy is approximately n × 10⁻⁴ eV. Find n.

G1 Physics · Accepted Answer

Step 1 — Photon momentum: p = Eγ/c. Conservation of momentum gives the recoiling atom equal momentum magnitude. Step 2 — Recoil kinetic energy: K = p²/(2M) = Eγ²/(2Mc²). Step 3 — Convert energies to eV: Eγ = 6.4×10³ eV and Mc² ≈ 56×931.5×10⁶ eV. K ≈ (6.4×10³)²/[2×56×931.5×10⁶] eV ≈ 3.93×10⁻⁴ eV. Step 4 — Identify integer: n≈4. Answer: 4.